Related papers: A note on combining chaotic dynamical systems usin…
The loss of synchronizability at large coupling strength is of major concern especially in the fields of secure communication and complex systems. Because theoretically, the coupling mode that can surely stabilize the chaotic/hyperchaotic…
Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…
Cyber-physical systems are often safety-critical and their correctness is crucial, as in the case of automated driving. Using formal mathematical methods is one way to guarantee correctness. Though these methods have shown their usefulness,…
With the constant increase of the number of autonomous vehicles and connected objects, tools to understand and reproduce their mobility models are required. We focus on chaotic dynamics and review their applications in the design of…
In this paper, an electronic circuit implementation of a robustly chaotic two-dimensional map is presented. Two such electronic circuits are realized. One of the circuits is configured as the driver and the other circuit is configured as…
In this study, we propose a fuzzy system for conducting short-term transactions in the forex market. The system is designed to enhance common strategies in the forex market using fuzzy logic, thereby improving the accuracy of transactions.…
Conventional techniques for compression and encryption are frequently laborious and resource-intensive, rendering them inappropriate for real-time applications. A plethora of research has been presented in the current literature to address…
We observe chaotic dynamics in a damped linear oscillator, which is driven only at certain regions of phase space. Both deterministic and random drives are studied. The dynamics is characterized using standard techniques of nonlinear…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
In previous work, the $k$-logistic map [Machicao and Bruno, Chaos, vol. 27, 053116 (2017)] was introduced as a transformation operating in the $k$ less significant digits of the Logistic map. It exploited the map's pseudo-randomness…
Here, we introduce a novel method for obtaining chaotic dynamics based on the Montgomery conjecture for the pair correlation of zeros of the Riemann zeta function. Motivated by the conjecture, we present a recursive relation that reveals…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
We study the encryption and decryption processes of color images using the synchronization of polarization dynamics in a free-running vertical-cavity surface-emitting laser (VCSEL). Here, we consider a bidirectional master-slave…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
In this paper, a sliding mode controller is designed to synchronize a chaotic fractional-order system. To construct a corrective control input, a saturation function sat(.), with a modified sliding surface is proposed. Finally, Chaos in the…
We present an introduction to the study of chaos in discrete and continuous dynamical systems using the CAS Maxima. These notes are intended to cover the standard topics and techniques: discrete and continuous logistic equation to model…
This paper discusses mixing of chaotic systems as a dependable method for secure communication. Distribution of the entropy function for steady state as well as plaintext input sequences are analyzed. It is shown that the mixing of chaotic…
A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises.…
It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behavior. This behavior can be used to design analogs of more complex logic families and some…